Investigating temporal field sampling strategies for site-specific

Hydrol. Earth Syst. Sci., 19, 3203–3216, 2015

www.hydrol-earth-syst-sci.net/19/3203/2015/

doi:10.5194/hess-19-3203-2015

© Author(s) 2015. CC Attribution 3.0 License.

Investigating temporal field sampling strategies for site-specific

calibration of three soil moisture–neutron intensity

parameterisation methods

J. Iwema1, R. Rosolem1,2, R. Baatz3, T. Wagener1,2, and H. R. Bogena3

1Department of Civil Engineering, University of Bristol, Queen’s Building, Bristol, UK2Cabot Institute, University of Bristol, Bristol, UK3Agrosphere (IBG-3), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany

Correspondence to: J. Iwema ([email protected])

Received: 29 January 2015 – Published in Hydrol. Earth Syst. Sci. Discuss.: 24 February 2015

Revised: 18 June 2015 – Accepted: 9 July 2015 – Published: 24 July 2015

Abstract. The Cosmic-Ray Neutron Sensor (CRNS) can

provide soil moisture information at scales relevant to hy-

drometeorological modelling applications. Site-specific cali-

bration is needed to translate CRNS neutron intensities into

sensor footprint average soil moisture contents. We investi-

gated temporal sampling strategies for calibration of three

CRNS parameterisations (modifiedN0, HMF, and COSMIC)

by assessing the effects of the number of sampling days and

soil wetness conditions on the performance of the calibration

results while investigating actual neutron intensity measure-

ments, for three sites with distinct climate and land use: a

semi-arid site, a temperate grassland, and a temperate for-

est. When calibrated with 1 year of data, both COSMIC and

the modified N0 method performed better than HMF. The

performance of COSMIC was remarkably good at the semi-

arid site in the USA, while the N0mod performed best at the

two temperate sites in Germany. The successful performance

of COSMIC at all three sites can be attributed to the bene-

fits of explicitly resolving individual soil layers (which is not

accounted for in the other two parameterisations). To better

calibrate these parameterisations, we recommend in situ soil

sampled to be collected on more than a single day. However,

little improvement is observed for sampling on more than

6 days. At the semi-arid site, the N0mod method was cali-

brated better under site-specific average wetness conditions,

whereas HMF and COSMIC were calibrated better under

drier conditions. Average soil wetness condition gave better

calibration results at the two humid sites. The calibration re-

sults for the HMF method were better when calibrated with

combinations of days with similar soil wetness conditions,

opposed to N0mod and COSMIC, which profited from using

days with distinct wetness conditions. Errors in actual neu-

tron intensities were translated to average errors specifically

to each site. At the semi-arid site, these errors were below the

typical measurement uncertainties from in situ point-scale

sensors and satellite remote sensing products. Nevertheless,

at the two humid sites, reduction in uncertainty with increas-

ing sampling days only reached typical errors associated with

satellite remote sensing products. The outcomes of this study

can be used by researchers as a CRNS calibration strategy

guideline.

1 Introduction

Soil moisture is an important state variable in land–

atmosphere interaction processes (Robinson et al., 2008),

ecosystem structure, function, and diversity (especially in

drylands, Rodriguez-Iturbe and Porporato, 2004), and a key

factor in agriculture (Siebert et al., 2005; Robinson et al.,

2008; Seneviratne et al., 2010). Traditionally, soil moisture

content has been measured mainly with point-scale sensors

(∼ 2 dm) (Topp and Ferré, 2002) or satellite sensors (e.g.

Soil Moisture and Ocean Salinity (SMOS), Kerr et al., 2001)

(2500–25 000 km2). This leaves a gap at intermediate scales

(∼ 1 km), relevant to hydrometeorological modelling and ap-

plications, and small watershed-scale studies (0.1–80 km2)

Published by Copernicus Publications on behalf of the European Geosciences Union.

3204 J. Iwema et al.: Temporal field sampling strategies for CRNS

(Wood et al., 2011; Robinson et al., 2008; Vereecken et al.,

2008).

A recent technology that may help fill this scale gap, is

the Cosmic-Ray Neutron Sensor (CRNS) (Zreda et al., 2008,

2012). The CRNS detects fast neutrons, which are produced

from high-energy neutrons of cosmic origin and are further

attenuated as they travel through the soil (Hess et al., 1961;

Zreda et al., 2008). Because of the high attenuation power of

hydrogen for these cosmic-ray neutrons, fast neutron inten-

sity decreases with increasing hydrogen content within the

sensor footprint (Zreda et al., 2008). Through this inverse

relationship with hydrogen content, fast neutron intensity is

non-linearly related with soil moisture content (Zreda et al.,

2008). The sensor footprint has a horizontal effective area

of about 600 m diameter at sea level for dry air but changes

slightly with elevation and soil moisture content in the atmo-

sphere (Desilets and Zreda, 2013). The measurement depth

varies between about 12 (wet conditions) and 76 cm (dry con-

ditions) (Zreda et al., 2008).

Site-specific neutron intensity–soil moisture relationships

should be determined to derive soil moisture values, i.e. the

CRNS needs site-specific calibration. The fully empirical N0

formula (Desilets et al., 2010) is usually deployed for this

calibration (Zreda et al., 2012). However, not only soil mois-

ture content affects the fast neutron intensity (Franz et al.,

2013c). All other hydrogen pools, (e.g. biomass, snow) af-

fect the signal, complicating the finding of a unique rela-

tionship between neutron intensity and soil moisture con-

tent for a variety of sites and conditions (Zreda et al., 2012).

Therefore a universal calibration function, the hydrogen mo-

lar fraction method (HMF), was developed, which assumes

a relationship between hydrogen prevalence and neutron in-

tensity (Franz et al., 2013b). While N0 and HMF both calcu-

late an integrated, depth-weighted profile average soil mois-

ture content, the COsmic-ray Soil Moisture Interaction Code

(COSMIC) computes neutron intensities from soil moisture

profiles (Shuttleworth et al., 2013) and can be directly ap-

plied in the context of hydrometeorological data assimilation

(Rosolem et al., 2014).

Typically only a single parameter (N0) of the N0-method

needs to be calibrated with a single point from average

soil moisture, representative of the CRNS footprint (Desilets

et al., 2010; Zreda et al., 2012). A similar approach is typ-

ically used for HMF, although estimates of additional hy-

drogen pools are also needed (Franz et al., 2013b). Orig-

inally, COSMIC was site-calibrated against neutron parti-

cle transport model Monte Carlo N-Particle eXtended (MC-

NPX, Pelowitz, 2005), using 22 hypothetical profiles cover-

ing a range of possible soil moisture profiles, but weighted

towards the more probable profiles at each considered site

(Shuttleworth et al., 2013).

Although a number of investigations have used single cal-

ibration points from measured soil moisture profiles for each

of the three methods (Rivera Villarreyes et al., 2011; Zreda

et al., 2012; Franz et al., 2013c; Bogena et al., 2013; Baatz

et al., 2014), to our record, there has been no previous study

on whether this is feasible for each of these three methods

at distinct sites. The fact that hydrogen pools (e.g. biomass,

litter layer water) vary differently over time than soil mois-

ture content profiles, and that not all these hydrogen pools

can always be monitored completely and accurately (Bogena

et al., 2013; Rivera Villarreyes et al., 2011), could be a com-

plicating factor. Therefore we posed the following research

questions:

– What are the benefits and limitations of the three dif-

ferent soil moisture–neutron intensity parameterisation

methods (N0, HMF and COSMIC) across sites with dis-

tinct climates and land cover types?

– How often should soil moisture profiles be sampled

in order to reliably calibrate the three soil moisture–

neutron intensity parameterisation methods?

– Under what type of wetness conditions or combina-

tions of wetness conditions should soil moisture profiles

be sampled in order to reliably calibrate the three soil

moisture–neutron intensity parameterisation methods?

In order to answer these questions, we calibrated the three

parameterisation methods for three sites with distinct types

of land cover and climate: a semi-arid, sparsely vegetated

site, a humid grassland, and a humid spruce forest. We used

data from 2012 to evaluate whether different days or differ-

ent combinations of days would lead to different calibration

results and to investigate our hypothesis that a single cali-

bration day is not always sufficient. We used depth-weighted

average soil moisture content to see whether wetness condi-

tions affect calibration results, and whether combinations of

days with different wetness conditions would yield different

calibration results.

2 Materials and methods

2.1 Methodology

We calibrated the three methods with different numbers of

sampling days: 1, 2, 4, 6, 10, and 16. The 1 day sampling

strategy (1DAY) corresponds to using a single, randomly se-

lected day within the time series to calibrate each method; the

2 days strategy (2DAY) is based on a pair of days randomly

selected from the time series, and so on. We compared these

temporal sampling strategies (see Table 1 for all abbrevia-

tions) with a reference strategy in which all available days

from the year 2012 were used to calibrate the three methods.

As a proxy for soil moisture samples, we used data from in

situ soil moisture sensor networks, because continuous soil

moisture sampling over a full year is usually not available.

It is however important to emphasise that distributed sensor

networks are not necessarily needed to be co-located with the

CRNS for operational purposes, including calibration. The

Hydrol. Earth Syst. Sci., 19, 3203–3216, 2015 www.hydrol-earth-syst-sci.net/19/3203/2015/

J. Iwema et al.: Temporal field sampling strategies for CRNS 3205

Table 1. Temporal sampling strategies and their theoretical numbers

of combinations.

Strategy Number of days Theoretical number of

from data series combinations for

Santa Rita Creosote (SR)

1DAY any 1 day 362

2DAY any combination of 2 days 6.5× 104





combined use of CRNS and sensor networks has been essen-

tial for understanding and improving this technology (Franz

et al., 2013b; Rosolem et al., 2014; Bogena et al., 2013; Baatz

et al., 2014). Despite having slightly different uncertainties

compared to gravimetric/volumetric soil samples obtained in

the field, in situ sensors have been already successfully used

in previous studies for comparison of CRNS and smaller-

scale soil moisture sensors (Franz et al., 2012; Bogena et al.,

2013; Baatz et al., 2014).

2.2 Site and data description

2.2.1 Santa Rita Creosote (SR)

Santa Rita Creosote (Table 2 and Fig. 1), hereinafter referred

to as SR, is a semi-arid site in Arizona, USA (Scott et al.,

1990), which is sparsely vegetated (∼ 24 % of surface area)

with creosote bush (∼ 14 % of surface area) and other species

of bushes, grasses, and cacti (Cavanaugh et al., 2011). Day-

time temperatures above 35 ◦C in summer and above 15 ◦C

in winter are common, and precipitation falls mostly in sum-

mer and winter (Scott et al., 1990; Franz et al., 2012). The

soil texture can be characterised as sandy loam with 5 to

15 % gravel (Cavanaugh et al., 2011). At SR 18 paired in

situ sensor profiles, with sensors (ACC-SEN-TDT, Acclima

Inc., Meridian,ID,USA) at 5, 10, 20, 30, 50, and 70 cm depth,

were installed with the spatial distribution as described by

Franz et al. (2012), with all equal horizontal weights (less

than 1 % of missing data). We computed a simple mean hor-

izontal soil moisture content for each sensor layer on every

day.

2.2.2 Rollesbroich (RB)

Rollesbroich (Table 2 and Fig. 1), located in Germany and

hereinafter referred to as RB, is a humid grassland site, dom-

inated by rye grass and smooth meadow grass (Baatz et al.,

2014). The seasonality in precipitation is small, with on av-

erage 540 mm in winter and 610 mm in summer (DWD,

2014). Average temperatures are 4.9 ◦C in winter and 10.9 ◦C

in summer (DWD, 2014). The soil contains mainly silt (∼

61 %) and some sand (∼ 20 %) and clay (∼ 18 %) (Qu et al.,

Figure 1. Maps and photos of the three research sites; Santa Rita

Creosote (SR), Rollesbroich (RB), and Wüstebach (WB). The cu-

mulative uncertainty contours indicate the relative areal contribu-

tions to the CRNS-signal. The 86 % contour represents the theoret-

ical CRNS footprint (Zreda et al., 2008).

2014). The in situ sensor network (SoilNet, Qu et al., 2013,

2014) consisted of 83 profiles with soil moisture sensors

(SPADE soil water content probes, sceme.de GmbH i.G.,

Horn-Bad Meinberg, Germany; Hübner et al., 2009) installed

at 5, 20, and 50 cm depth (with ∼ 15 % of missing data).

While the sensor profiles at SR were positioned such that

all had equal weights, this was not the case at RB, where

we calculated horizontal average daily soil moisture contents

by assigning weights to the sensor profiles representing their

distance to the CRS, as described in Bogena et al. (2013).

2.2.3 Wüstebach (WB)

Wüstebach (Table 2 and Fig. 1), hereinafter referred to as

WB, is a humid Norway spruce (90 % of surface area) for-

est test site in Germany, with little undergrowth (Etmann,

2009; Baatz et al., 2014). The seasonality in precipitation is

small, with on average 550 mm in winter and 650 mm in sum-

mer (DWD, 2014). Average temperatures are 4.5 ◦C in win-

ter and 10.5 ◦C in summer (DWD, 2014). The most preva-

lent soil texture is silty clay loam, containing a substantial

www.hydrol-earth-syst-sci.net/19/3203/2015/ Hydrol. Earth Syst. Sci., 19, 3203–3216, 2015


Table 2. Characteristics of the three study sites. Information for SR is from Shuttleworth et al. (2013); Franz et al. (2013b); Scott et al.

(1990); Cavanaugh et al. (2011); WRCC (2006). Information for RB and WB is from Baatz et al. (2014).

Site Latitude Longitude Altitude Pavg Tavg ρs lw + wSOM AGBwet

(dec. degr.) (dec. degr.) (ma.s.l.) (mmy−1) (◦C) (gcm−3) (cm3 cm−3) (kgm−2)

Santa Rita Creosote (SR) 31.9085◦ N 110.839◦W 989 415 17.8 1.46 0.041 1.12

Rollesbroich (RB) 50.6219◦ N 6.304◦ E 515 1300 7.9 1.09 0.067 0.70

Wüstebach (WB) 50.5035◦ N 6.333◦ E 615 1400 7.5 0.83 0.068 68.2

amount of coarse material in the deeper parts, and a litter

layer of variable depth (0.5 to 14 cm) (Bogena et al., 2014).

150 profiles with in situ soil moisture sensors (horizontally

installed ECH2O sensors (EC-5 and 5TE, Decagon Devices

Inc., Pullman, USA), SoilNet, Rosenbaum et al., 2012) at 5,

20, and 50 cm depth were installed (with ∼ 23 % of missing

data). Horizontal averaging was done with the same distance-

weighting method as for RB. Because snow layers com-

plicate the interpretation of CRNS soil moisture estimates

(Zreda et al., 2012), days with snow cover were omitted for

both German sites, RB, and WB (Baatz et al., 2014), while

at SR no snow cover was recorded.

2.2.4 CRNS and in situ soil moisture data

preprocessing

The same CRNS model (CRS-1000, Hydroinnova LLC, Al-

buquerque, NM, USA) was used at all sites. We corrected the

CRNS observed neutron intensities at each site for variation

in high-energy neutron intensity, atmospheric pressure, and

atmospheric water vapour content (Rosolem et al., 2013), fol-

lowing the suggestions of Zreda et al. (2012) and Baatz et al.

(2014). To simulate a single day soil sampling campaign, we

used daily average soil moisture contents from each in situ

soil moisture sensor layer and daily average neutron intensi-

ties (Fig. 2).

2.3 Soil moisture–cosmic-ray neutron

parameterisations

2.3.1 Modified N0 method

The N0 method was originally developed by Desilets et al.

(2010), using MCNPX. Bogena et al. (2013) introduced

some changes to the N0 method by taking into consideration

dry soil bulk density to calculate the volumetric water con-

tent, and adding lattice water and soil organic matter water

equivalent (Eq. 1):

θ =a0 · ρs

Npih/N0− a1

− a2 · ρs− lw−wSOM, (1)

where the parameter values a0 = 0.0808 (cm3 g−1), a1 =

0.372 (−), a2 = 0.115 (cm3 g−1), and N0 (cph) is a site-

dependent normalisation parameter. Parameters lw and

wSOM are the CRNS-footprint average volumetric lattice wa-

Figure 2. Precipitation (P ) and in situ sensor soil moisture content

(θ ) time series from the three research sites.

ter content and soil organic matter equivalent water content

(cm3 cm−3) respectively, and ρs (gcm−3) is the dry soil bulk

density, usually determined from soil samples. Npih is cor-

rected fast neutron intensity and θ is CRNS footprint average

volumetric soil moisture content (cm3 water cm−3 soil).

In order to better compare the results with the HMF and

COSMIC methods, we have rearranged terms in the N0mod

formulation, so that neutron intensities are calculated based

on given soil moisture. However, our preliminary results in-

dicated that the N0 method failed to accurately estimate the

soil moisture measurements consistent to the sites (results

not shown). The likely reason was the fixed coefficients de-

fined in the equation which was also found by Rivera Vil-

larreyes et al. (2011). We therefore modified Eq. (1), giving

Eq. (2).

Npih =b0 · ρs

θ + lw+wSOM+ b2 · ρs

− b1 (2)

This equation contains parameters b0 (cph cm3 g−1),

b1 (cph), and b2 (cm3 g−1), which all need site-specific

calibration. We hereinafter refer to this equation as the

modified N0 method (N0mod).

We calculated depth-weighted profile average soil mois-

ture contents with the methods proposed by Bogena et al.

(2013) to consider exponentially decreasing weights (ws)



with depth (Eq. 3):

ws = 1− e−zy (3)

and

y =−5.8

ln(0.14) · (Hp+ 0.0829), (4)

where z represents the measurement depth (cm) and Hp rep-

resents the total below ground hydrogen pool in the respec-

tive soil layer in g H2O cm−3. For a more detailed description

we refer to Bogena et al. (2013).

2.3.2 Hydrogen Molar Fraction (HMF) method

The HMF method was first developed to avoid site-specific

calibration of the CRNS where soil sampling is difficult

and also to facilitate the application of the mobile cosmic-

ray soil moisture sensors (i.e. rover applications) (Franz

et al., 2013b). In such cases soil moisture could be calcu-

lated provided neutron intensity and other hydrogen sources

are known. However, for sites for which reliable soil mois-

ture samples can be obtained, the HMF method can also be

used for site-specific calibration of the CRNS. In the HMF

method, the fast neutron intensity is calculated with Eq. (5):

Npih =Ns ·

{3.007e(−48.391·hmf)

+ 3.499e(−5.396·hmf)}, (5)

where the values of the coefficients were revised accord-

ing to McJannet et al. (2014). hmf is∑(H)/

∑(Eall) is to-

tal hydrogen molar fraction (mol H/total mol).∑(H) is the

sum of all hydrogen (mol), including hydrogen in above-

ground biomass, lattice water hydrogen, hydrogen in and

bound to soil organic matter, and soil water hydrogen; and∑(Eall) (mol) is the sum of all elements: atmospheric N and

O, soil solids (quartz), lattice water, soil organic matter wa-

ter equivalent, soil water, above-ground biomass, (cellulose)

and above-ground biomass water.Ns (cph) is a normalisation

parameter which needs to be site-calibrated.

We employed HMF following the same approach rec-

ommended by Franz et al. (2013b), and calculated average

profile soil moisture contents with the same depth weight-

ing method used for the N0mod method. We neglected root

biomass, and litter layers. To calculate total amounts of

chemical elements, we used a horizontal footprint radius of

335 m for all three sites (Franz et al., 2013b). We calculated

measurement depths with the method from Bogena et al.

(2013).

2.3.3 COSMIC

COSMIC was developed as a data assimilation forward op-

erator, and is a simpler, computationally less expensive fast

neutron transport model than MCNPX (Shuttleworth et al.,

2013; Rosolem et al., 2014). COSMIC considers three pro-

cesses: (1) exponential decay of high-energy neutron inten-

sity with depth, (2) creation of fast neutrons as a consequence

Figure 3. Relationship (red line) between soil bulk density ρs

(gcm−3) and COSMIC parameter L3 (gcm−2), adapted from Shut-

tleworth et al. (2013). Two volcanic Hawaïan sites from Shuttle-

worth et al. (2013) were discarded in this case because of their aber-

rant physical characteristics.

of collisions with soil and water particles and (3) exponen-

tial decay of fast neutrons while they travel upward from the

place where they were created. COSMIC can be written as

follows (Eq. 6):

Npih =N

∞∫0

[e

(−

[ms(z)L1+mw(t,z)L2

])· [αρs+ θ(t,z)+ lw+wSOM]

·2

π·

π2∫

0

e

(−1

cos(β)

)·

[ms(z)L3+mw(t,z)L4

]dβ

]dz, (6)

where β (−), L1 = 162.0 (gcm−2), L2 = 129.1 (gcm−2),

and L4 = 3.16 (gcm−2) are universal parameter values, and

L3 (gcm−2), N (cph), and α (−) are site-dependent parame-

ters. The parameters mw and ms are the integrated mass per

unit area (gcm−2) of dry soil and water respectively and ρs

and ρw are the dry soil bulk density and soil water density

(gcm−3). In the original model, the soil water included soil

moisture and lattice water (Shuttleworth et al., 2013), while

Baatz et al. (2014) added soil organic matter water equivalent

to this. We used an empirical relation with a high correlation

(r2= 0.995 (−)) between parameter L3 and soil bulk den-

sity (ρs) (see Fig. 3) to derive values for L3 at the three sites.

Hence, we calibrated only parameters N and α in this study.

2.4 Calibration methodology

To investigate our first research question (“What are the ben-

efits and limitations of the three parameterisations across dis-

tinct climates and land cover types?”), we introduced a ref-

erence strategy: for each site, we calibrated each parameteri-

sation using all available days of the year 2012. This yielded

one best solution for each site/parameterisation combination,

against which we compared the results from other six sam-



pling strategies (Table 1). We calibrated the parameterisa-

tions, for the 1DAY strategy, for each site, for each day of the

year, resulting in as many calibration solutions as there were

days with data. While we could calibrate the parameterisa-

tions for the 2DAY temporal strategy for all possible combi-

nations of different days (65 000, 47 895, and 39 060 for SR,

RB, and WB, respectively), for the higher order strategies

this would, in theory, have resulted in an impractical num-

ber of combinations and consequently be highly expensive

computationally (Table 1). Therefore, we drew random sam-

ples of day combinations, equal in size to the total number

of combinations of the 2DAY strategy, from the populations

of possible combinations. To investigate whether the chosen

sample sizes were sufficiently large, we drew for each param-

eterisation and each site, for the 4DAY and 16DAY strategies,

four extra random samples of the same size. Additionally, we

drew samples with different numbers of day combinations

(500, 5000, 50 000, 200 000, 1 000 000) for each parameter-

isation at each site. The results of both tests (not shown) in-

dicated that using sample sizes of 65 000, 47 895, and 39 060

for SR, RB, and WB respectively, was sufficient for our anal-

yses.

To determine parameter calibration ranges for the N0mod

method, we first applied relatively wide ranges (b0: 25–1000,

b1: 10–3000, and b2: 0.01–1.0) based on the original val-

ues of parameters a0, a1, and a2 and values of N0 from

the COsmic-ray Soil Moisture Observing System (COS-

MOS) (Zreda et al., 2012; data available at http://cosmos.

hwr.arizona.edu/) and Baatz et al. (2014). Using the initial

ranges, we calibrated the N0mod method against soil mois-

ture content – neutron intensity combinations obtained from

COSMIC simulations for each of these sites. We used a range

(θ varying from zero to 0.50 cm3 cm−3 increments) of homo-

geneous soil moisture profiles as input for COSMIC to calcu-

late the neutron intensities for COSMOS sites from Shuttle-

worth et al. (2013) (except two volcanic Hawaïan sites) and

the two German sites used in this study. We used COSMIC

parameter values from calibration against MCNPX (Shuttle-

worth et al., 2013) for this purpose, and added the two Ger-

man sites with parameter values from Baatz et al. (2014)

because these showed, in contrast with the COSMOS sites,

neutron intensities below 750 (cph). The resulting parameter

ranges were smaller than the initial ranges and were used in

our analyses (Table 3). We constructed a calibration range

for HMF parameter Ns (Table 3) using the values reported

by Franz et al. (2013b) and Baatz et al. (2014), and we based

the parameter calibration ranges for COSMIC (Table 3) on

the values found by Shuttleworth et al. (2013) and Baatz et al.

(2014).

A total of 100 000 parameter sets were sampled from the

parameter space of the N0mod method, 5000 for the HMF

method, and 200 000 for COSMIC, using Latin hypercube

sampling (LHS). We ran the parameterisations with these

generated parameter sets for each day, and simulated the neu-

tron intensity. We calculated the absolute error (AE) for the

Table 3. Parameter ranges for the three parameterisations used in

this study.

Method Parameter Lower bound Upper bound

N0mod b0 (cphcm3 g−1) 35 800

b1 (cph) 300 1700

b2 (cm3 g−1) 0.02 0.15

HMF Ns (cph) 200 2000

COSMIC N (cph) 50 1500

α (−) 0.2 0.4

1DAY strategy, and the mean absolute error (MAE) for the

multiple day strategies. The best solution for each day was

found by selecting the parameter set which gave the lowest

AE or MAE. To compare the overall performance through-

out the whole year of a given calibrated parameterisation, we

computed the MAE over all available days (with respect to

simulated and observed neutron intensities) of 2012, for each

best solution, hereinafter referred to as MAEval.

3 Results and discussion

3.1 Identification of strengths and weaknesses of the

three parameterisations when calibrated against all

available data

Figure 4 shows calibration results using all three parame-

terisations, at the three sites. The simulated neutron inten-

sities closely matched the observed neutron intensities with

relative errors (MAEval divided by mean neutron intensity)

between 1 and 2 %. However, at SR, observed neutron in-

tensities were systematically overestimated (by 1 to 8 %) by

all three parameterisations during the monsoon (mid July–

mid September) and underestimated between mid November

and mid December (by 2 to 6 %). Additionally, from early

January until mid March, HMF and COSMIC matched the

observed fast neutron intensities well, while N0mod under-

estimated fast neutron intensity by up to 3 % for N0mod. At

RB,N0mod seemed to have yielded the best calibration result,

while HMF and COSMIC showed some periods of both over-

and underestimation with absolute errors up to 28 cph. Fi-

nally, at WB the calibration solution for HMF seemed to have

had slightly more difficulty simulating the observed neutron

intensities, although neutron intensity variation (standard de-

viation (SD) of 9.4 cph) was more similar to the observed

variation (SD of 9.2 cph) than the other two parameterisa-

tions (SD of 7.2 cph for N0mod, and 7.7 cph for COSMIC).

Although at SR more daily neutron intensity estimations

were outside the observed uncertainty bounds (e.g. 63 % for

HMF at SR and 6 % at WB), we note that this is due to the

relatively lower uncertainty caused by the higher observed

neutron intensities (Zreda et al., 2008). Overall, N0mod per-

formed best at the two temperate sites, HMF showed slightly


http://cosmos.hwr.arizona.edu/

http://cosmos.hwr.arizona.edu/


Figure 4. Neutron intensity time series for the calibration solutions

from the reference strategy plotted with observed neutron intensities

with uncertainty bounds. The uncertainty boundaries represent 95 %

confidence intervals around the mean daily fluxes. MAEval values

of each parameterisation are shown in the same colour used for the

neutron intensity time series.

poorer results at all three sites, and COSMIC performed best

at the semi-arid site, and average at the two temperate sites.

The periods of over/underestimation for all parameterisa-

tions at SR could indicate either limitations with the param-

eterisations used or with the quality of measurements used.

The differences between the best solutions of the three pa-

rameterisations for certain periods, found at all three sites,

might be related to differences in parameterisation complex-

ity. Where COSMIC performed better compared to the two

other methods, this could indicate the benefits of explicitly

resolving individual soil layers, as opposed to using depth-

weighted soil moisture as employed by the other two meth-

ods. Explicitly taking into consideration the depth-varying

SOM and lattice water content could potentially improve

measurement depth and neutron intensity estimates.

To get a better idea of how good the best solutions from

the reference strategy actually were, we compared them with

calibration results obtained from previous research; see Fig. 5

and Table 4. The originalN0 solution (only parameterN0 cal-

ibrated) for SR was taken from the COSMOS website (Zreda

et al., 2012), for HMF from Franz et al. (2013a) and for

COSMIC from the MCNPx calibrations from Shuttleworth

et al. (2013). We took all original solutions for RB and WB

from Baatz et al. (2014). Only parameter N was calibrated

for COSMIC at RB and WB (Baatz et al., 2014), while pa-

rameters L3 and α were computed with relationships from

Shuttleworth et al. (2013). The original solutions matched

the observed neutron intensities less satisfactorily when com-

pared to the best solutions from the reference strategy em-

ployed in this study. The most striking difference is that N0

at SR was not able to match the observed neutron intensities

Figure 5. Neutron intensity time series for the calibration solutions

from the reference strategy (Ref.) and from original (Orig.) calibra-

tion solutions plotted together with observed neutron intensities and

associated uncertainty bounds. MAEval,orig (cph) values for origi-

nal solutions are included.

because of the shape of the neutron intensity–soil moisture

relationship defined by parameters a0, a1, and a2 (notice this

was one of the main motivations for introducing the modi-

fied N0 method, as discussed in Sect. 2.3.1). As mentioned

in Sect. 2.3.1 for our preliminary results, this suggests that

using the fixed parameter values for a0, a1, and a2 should

be investigated locally. At RB the original COSMIC solution

was clearly worse than our reference strategy solution and at

WB this occurred for HMF and COSMIC at WB.

To identify the reasons for the relatively worse perfor-

mance of the original solutions of HMF and COSMIC at RB

and WB, we compared these with calibration solutions for

which we used the same single days, but with our model

and calibration settings (in situ soil moisture data, COS-

MIC with both parameters N and α calibrated). The differ-

ences between the original and reference solution of HMF

seemed to have been caused by the different values for the

HMF coefficients and the chosen sampling days. The main

cause for the systematic underestimations by COSMIC was

that Baatz et al. (2014) calibrated only parameter N , since

our solutions using the same days performed clearly bet-

ter (MAEval = 7.6 cph at RB; 5.0 cph at WB; compare to

12.2 cph and 9.8 cph, respectively, from the original calibra-

tion).

3.2 Assessing a suitable soil sampling frequency for the

three methods

In Fig. 6, the 25, 50, and 75 percentiles of the MAEval pop-

ulations of best solutions are represented by dots, for each

temporal strategy. The MAEval values of the best solutions of

the reference temporal strategy are indicated with coloured



Table 4. Parameter values for the best solutions of the reference strategy (Ref.) and the original (Orig.) solutions. Parameters a0, a1, and a2

are constants in the original N0 (Desilets et al., 2010) and are hence not shown. For the original HMF solutions, the coefficients used were

defined by Franz et al. (2013b).

Site N0mod N0 HMF COSMIC

b0 b1 b2 N0 Ns N α L3

Ref. Orig. Ref. Orig. Ref. Orig Ref. Orig Ref. Orig

SR 122 1004 0.028 2945 870 1003 469 390 0.200 0.251 113.5 114.8

RB 61 504 0.062 1208 478 494 247 213 0.201 0.293 76.6 76.6

WB 44 384 0.021 936 706 669 195 166 0.201 0.320 50.8 50.8

Figure 6. 25, 50, and 75 percentiles of MAEval best solution popu-

lations. The coloured horizontal lines represent the MAEval values

for the calibrated solutions from the reference strategy.

horizontal lines. This figure can be interpreted as such that

25 % of the best solutions of a population had an MAEval

equal to or smaller than the MAEval of the 25 percentile,

the 50 % best calibration solutions had values smaller than

the 50 percentile MAEval, etcetera. The MAEval value of the

25 percentile hence tells us how good the better solutions

were; a low value means the chance of obtaining a good solu-

tion was high. A MAEval value for the 75 percentile closer to

the 50 and 25 percentiles means the overall range of solutions

was reduced, and hence the chance of obtaining a relatively

poor performance due to calibration was relatively small.

We see that for the 1DAY strategy at SR, for all three per-

centiles, the MAEval values of N0mod were higher than those

of HMF and COSMIC (by approximately 1.5 to 2 times).

However, subsequent increase of the number of days used,

made the results of N0mod approach those of HMF. At 6DAY

the MAEval ofN0mod was less than 1.2 times higher than that

of HMF only. As expected, with increasing number of sam-

pling days, the population range was reduced for all three

parameterisations, and hence also the chance of obtaining

poor solutions decreased. The differences between the tem-

poral strategies were smallest for HMF at all three sites: be-

Figure 7. Soil moisture–neutron intensity relationship derived from

reference calibration for all studied sites using three distinct param-

eterisations. Extrapolated curves are shown as dashed lines.

tween 1DAY and 16DAY, MAEval values of HMF got up to

1.6 times smaller, while MAEval values of e.g. COSMIC got

up to 2.2 times smaller.

From the 75 percentiles we see that the MAEval values for

all three parameterisations flattened out between the 6DAY

and the 10DAY strategy, after improvements of between 1.3

and 2.2 times. After these sharp decreases, little improve-

ments (up to 1.2 times) were made by increasing the num-

ber of days to those of the reference solutions. From a field-

work perspective, this means that despite the strong increase

in work effort, only a small improvement in parameterisa-

tion quality will be gained. The quicker improvement (to rel-

atively poor reference strategy solutions), and smaller differ-

ences between the temporal strategies of HMF could be due

to the fact that HMF contains only one free parameter.

Researchers have traditionally interpreted soil moisture er-

ror values rather than neutron intensity errors. We have there-

fore translated the neutron intensity errors into soil moisture

content errors for clarity. We took the mean observed neu-

tron intensity at each site and used the reference solutions to

compute soil moisture content error estimates (Fig. 7). For



Figure 8. Estimated errors in soil moisture representing the

75 percentiles obtained by calibrating against observed neutron in-

tensities. The coloured horizontal lines represent the estimated er-

rors from the reference strategy. The grey solid and dashed lines

represent the typical errors found in point-scale sensors (TDT) and

satellite remote sensing products (e.g. SMOS) respectively.

that purpose we subtracted or added the MAE neutron values

from the mean observed neutron intensity and then projected

onto the vertical axis of Fig. 7 to obtain soil moisture differ-

ences using the reference solution curves. We did this for the

75 percentiles only. We compared them with typical errors of

time domain transmissivity (TDT) sensors (0.02 cm3 cm−3,

Topp et al., 2001) and with those from satellite remote sens-

ing products such as SMOS and SMAP (0.04 cm3 cm−3, Kerr

et al., 2001). We hence assumed a 75 % chance of obtaining

a calibration result, which was equal to, or better than these

thresholds, sufficiently reduces the uncertainty. For simplic-

ity, in order to obtain curves representing the COSMIC refer-

ence solutions, we assumed homogeneous soil moisture pro-

files. However, the different curves for each site had differ-

ent slopes (e.g. HMF flatter at RB and WB), which would

introduce mixed results not necessarily relevant to the over-

all behaviour analysed for each site. We hence had to choose

one curve per site to estimate soil moisture errors, shown in

Fig. 8. We chose N0mod for two reasons. Firstly, it yielded

the best reference solutions at RB and WB. Secondly, while

COSMIC was best at SR, to obtain soil moisture error esti-

mates, the need to use homogeneous profiles for this model

makes representing it with a single curve an approxima-

tion only. Choosing HMF or COSMIC would have yielded

slightly different error magnitudes only because the curves

are only slightly different within the range at which obser-

vations are available for each individual site. This is indi-

cated by relatively similar correlation coefficients calculated

between observed and individual curves (not shown).

Figure 9. Parameter range distributions obtained for the best so-

lution populations for the N0mod parameters (b0, b1, and b2). The

parameter values of the reference strategy solutions are represented

by black horizontal lines.

On average, all computed errors were below the two im-

posed thresholds at SR. At RB and WB the magnitude of

the errors was always higher than the TDT threshold. At RB,

about 4 days would be needed for N0mod and HMF while for

COSMIC, 4 to 6 days would suffice to pass the SMOS thresh-

old. All three parameterisations needed about 10 days to

reach the SMOS threshold at WB. At SR, relatively low soil

moisture content error estimates were obtained because the

observations were limited to the dry range where the curve

is relatively flat and a large neutron intensity error translates

into a small soil moisture content error. At RB and WB in-

stead, observed soil moisture contents were limited to the wet

range and the curves are steeper than those at SR.

The distributions of the parameter values are shown in

Figs. 9 and 10. The 75 percentile ranges of b0 and b1

were reduced in size by 2 to 4 times for all parameterisa-

tion/site combinations with increased number of sampling

days. The parameter values satisfactorily approached the so-

lutions from the reference strategy (Table 4), with the excep-

tion of b2 at RB and WB. Parameter b2 probably specifies a

soil moisture content offset at the dry end of the soil moisture

content/neutron intensity curve. In Eq. (3) it is added (after

multiplication with ρs) to the soil moisture and lattice water

terms. While at SR the observations were in the dry range, at

RB and WB the wet range was observed only (Fig. 7). Hence,

the role of parameter b2 was probably less relevant for fitting

to the data. The 75 percentile parameter ranges of HMF and

COSMIC converged towards the parameter values from the

reference temporal strategy for all three sites.

In addition to the MAEval, we evaluated the coefficient

of determination (r2; results not shown), and the mean bias

(results not shown) with respect to the observed and simu-

lated neutron intensities of all days of 2012. While the mean



Figure 10. Parameter range distributions obtained for the best solu-

tion populations for HMF parameter Ns and COSMIC parameters

N , and α. The parameter values of the reference strategy solutions

are represented by black horizontal lines.

bias improved (decreased) clearly with increasing numbers

of sampling day, for all sites and methods (up to 20 times

smaller for reference solutions compared to 1DAY), r2 re-

mained nearly constant. These findings indicate that param-

eterisation dynamics, which are reflected in r2, are more

strongly conditioned by the input data whereas systematic

biases can be caused by poor parameter selection. The found

improvement of the MAEval with increasing number of sam-

pling days was hence due to reduced systematic biases. This

is important, because systematic biases in soil moisture may

hinder modelling applications (e.g. data assimilation, Dee,

2005; Reichle and Koster, 2004).

Calibrating with a single day appears to be insufficient to

guarantee accurate/acceptable parameterisation performance

for all three parameterisations at sites enduring predomi-

nantly wet soil conditions and relatively steep soil moisture

content/neutron intensity curves. The results for the reference

strategy and the other sampling strategies indicate thatN0mod

is more easily calibrated for sites with relatively low season-

ality in temperature and precipitation. HMF probably showed

least differences between few and many sampling days; it

only has one parameter that needs calibration. Moreover the

reference strategy yielded relatively poor calibration results

for HMF anyway. COSMIC performed relatively similarly

for sites with different vegetation cover, and precipitation and

temperature variability. A model with fewer parameters but

similarly or slightly worse performance may be preferred to

a more complex model.

For applications of mobile CRNS rovers (Chrisman and

Zreda, 2013; Dong et al., 2014), multiple calibration in-

stances are more difficult to be realised. However, in regions

where stationary CRNS are available, information from mo-

bile surveys can be better translated/constrained by such

Figure 11. Cumulative density functions (CDF) of sub-groups

from the 1DAY best solution MAEval populations, plotted against

weighted average soil moisture content (θ ) (Bogena et al., 2013).

sensors, and hence multiple-day calibration becomes even

more important for stationary sensors. Alternatively, one may

adopt a space-for-time approach such as those approaches

proposed for satellite remote sensing soil moisture applica-

tions (e.g. Reichle and Koster, 2004).

3.3 Evaluating preferred wetness conditions for

calibration

The required numbers of sampling days found in the previous

section could possibly be reduced if certain wetness states

that yield relatively poor calibration solutions are avoided,

and preferred wetness states for good sampling days are

chosen. To identify such preferred wetness states, we used

depth-weighted average soil moisture content (Bogena et al.,

2013) as an indicator of wetness conditions. We used the

cumulative density function (CDF) approach as employed

for parameter sensitivity analysis (Demaria et al., 2007), but

instead applied it to soil moisture content states. We split

the MAEval populations into groups of 25 % increments,

ranked from best (0–25 %) to worst (75–100 %). We calcu-

lated a CDF describing the distribution of weighted average

soil moisture contents for each of the MAEval groups for

the 1DAY temporal strategy (Fig. 11). We computed CDFs

describing the absolute difference between the soil moisture

contents of the paired days for the 2DAY strategy (Fig. 12),

while for the 4–16DAY strategies we used the SDs over the

soil moisture contents of the combined days. Notice that all

metrics are somewhat related to a dispersion measure from

the mean value (or the mean value itself for 1DAY), and are

hence related to each other. The figures can be understood

by realising that at soil moisture contents where the CDF

of a certain group is steep, relatively more solutions are ob-

tained.



Figure 12. Cumulative density functions (CDF) of sub-groups from

the 2DAY best solution MAEval populations, plotted against the dif-

ference (1) between the weighted average soil moisture contents

(θ ) of the paired days.

The CDFs of the 1DAY strategy showed differences be-

tween the 75–100 % solutions and the other groups for all

site–parameterisation combinations except N0mod and HMF

at WB. At SR, relatively dry conditions seemed to yield a bet-

ter chance of relatively good calibration solutions for HMF

and COSMIC; for instance, 50 % (CDF= 0.5 (−)) of the so-

lutions of the best 25 % group of both parameterisations had

θ < 0.035 cm3 cm−3, while 50 % of the solutions of the worst

25 % group had θ > 0.05cm3 cm−3. Relatively dry to aver-

age wetness conditions (0.03< θ < 0.04cm3 cm−3) yielded

relatively good calibration solutions for N0mod at SR. The

worst solutions (75–100 % groups) mostly originated from

relatively dry conditions (θ < 0.35cm3 cm−3) for all three

parameterisations at RB, while the better solutions (0–75 %

groups) were mostly obtained under average wetness condi-

tions (0.37< θ < 0.41cm3 cm−3). At WB this was only the

case for COSMIC. We therefore recommend avoiding rel-

atively dry conditions at RB and WB and to sample under

conditions more closely related to the average conditions of

those sites instead, if only a single day is used. It is unlikely

that the worse calibration solutions obtained under drier con-

ditions at RB and WB were caused by changes in above-

ground hydrogen pools (e.g. litter layer), because Bogena

et al. (2013) found that such hydrogen pools become less

dominant under drier conditions.

The calibration for N0mod and COSMIC at all three sites

was improved when paired days with distinct soil moisture

contents were used, because the CDFs of the groups of worst

(50–75 and 75–100 %) calibration solutions showed rela-

tively sharp increases for similar soil moisture contents (SR:

1θ < 0.01cm3 cm−3; RB and WB: 1θ < 0.05cm3 cm−3),

whereas better solutions were obtained under relatively drier

conditions (Fig. 12). This might be expected because dif-

ferent soil moisture profiles are taken into account, as well

as variations in other hydrogen pools. HMF showed no dif-

ferences at SR and somewhat opposite results at RB and

WB, where better solutions were relatively often obtained

from combinations of days with similar wetness conditions

(1θ < 0.05cm3 cm−3). Figures 13 (4DAY) and 14 (16DAY)

show that increasing the number of days decreased the ef-

fects of different wetness conditions of the constituting days.

Similar to the 2DAY strategy, for the 4DAY strategy differ-

ent wetness conditions were more likely to yield a relatively

good calibration solution for N0mod and COSMIC while for

HMF, different wetness conditions seemed to affect the re-

sults least.

A possible explanation for the opposite effects of wetness

variability on HMF compared to the other two parameterisa-

tions at RB and WB is the fixed shape of the HMF curves

as shown in Fig. 7. While the shapes of N0mod and COS-

MIC can change (different parameter values) when a wider

range of wetness conditions is covered, the shape of the HMF

curves cannot be adjusted by sampling a wider range of wet-

ness conditions and hence such practice may not always im-

prove results. Figure 7 also indicates the data were limited

to certain parts of the curves only and hence increasing the

differences between wetness conditions outside these ranges

could potentially reduce the needed number of sampling days

and/or increase the confidence about the calibration results

obtained.

Based on our results, we can conclude that the required

number of days could be limited by choosing appropriate

wetness conditions, or wetness variability. However, this is

mainly limited to the worst 25 % (i.e. 75–100 %) of the anal-

ysed results. The preferred choice depends on the site chosen

and the parameterisation used and hence no general recom-

mendation can be given.

4 Conclusions

We investigated the performance of three currently available

CRNS parameterisation methods (modified N0, HMF, and

COSMIC) at three sites characterised by distinct climate and

land use. When calibrated with data from all days available

from 1 year, the COSMIC and N0mod methods performed

slightly better than HMF at the two more temperate and hu-

mid sites, while at the semi-arid site, COSMIC performed

better than both other methods. The soil profile approach of

COSMIC gave an advantage at this site.

We found that it is advisable to collect soil moisture sam-

ples on more than a single day regardless of which param-

eterisation is used. However, sampling on more than 6 days

would, despite the strong increase in work effort, improve

parameterisation quality only a little. On average, observed

errors in soil moisture (translated from errors in neutron in-

tensities) showed that at the semi-arid site, the soil moisture




the 4DAY best solution MAEval populations, plotted against the SD

(σ ) of the weighted average soil moisture contents (θ ) of the com-

bined days (Bogena et al., 2013).


the 16DAY best solution MAEval populations, plotted against the

SD (σ ) of the weighted average soil moisture contents (θ ) of the

combined days (Bogena et al., 2013).

error is systematically below typical uncertainties observed

for point-scale and satellite remote sensing products regard-

less of number of sampling days. At both humid sites in Ger-

many, the increase in sampling days reduced the uncertainty

in translated soil moisture data to values similar or slightly

below those assumed for satellite remote sensing, but failed

to reach the same level of accuracy found in point-scale sen-

sors.

Sampling on days or combinations of days with appropri-

ate soil wetness conditions can reduce the required number of

sampling days. The preferred choice depends on the site and

the parameterisation used. At the semi-arid site, the N0mod

method was better calibrated better under average wetness

conditions, whereas HMF and COSMIC were calibrated bet-

ter under drier conditions. Average soil wetness conditions

gave higher chances for better calibration results for all three

parameterisations at the humid grassland site, and for COS-

MIC at the humid forest site. In addition, the calibration re-

sults for the N0mod and COSMIC method were better when

calibrated with combinations of days with distinct soil wet-

ness conditions. On the other hand, HMF was less affected

by distinct wetness conditions at the semi-arid site while per-

forming slightly better when using days with more similar

wetness conditions at both humid sites. These differences de-

creased with an increasing number of days and were almost

absent for the 16 days sampling strategy.

It is important to notice that varying the density and/or spa-

tial (vertical and horizontal) sampling of soil moisture mea-

surements may influence the calibration performance. The

analysis of the actual impact on performance is beyond the

scope of this study, which focuses on understanding the tem-

poral sampling using typical spatial soil sampling approaches

previously published in literature (Zreda et al., 2012; Desilets

and Zreda, 2013; Bogena et al., 2013).

By providing a first general guideline of how often and

under which wetness conditions soil moisture should be

sampled, the outcomes of this study will help researchers

to validate old calibration results and to reliably calibrate

new CRNS sites and such as in the UK, as part of the

AMUSED project (http://www.bris.ac.uk/news/2014/august/

soil-moisture-and-cosmic-rays.html). Our discussion on dif-

ferences between the three CRNS parameterisation methods

can be used to identify which parameterisation can be used

best to relate neutron intensities to footprint average soil

moisture contents.

Acknowledgements. This research was supported by the Queen’s

School of Engineering (University of Bristol) PhD scholarship.

Partial support for this work was also provided by the Natural

Environment Research Council (A MUlti-scale Soil moisture-

Evapotranspiration Dynamics study (AMUSED); grant number

NE/M003086/1). We gratefully acknowledge the support from

TERENO (Terrestrial Environmental Observatories) project

funded by the Helmholtz-Gemeinschaft. We also thank Shirley

Papuga (University of Arizona) and Trenton Franz (University

of Nebraska-Lincoln) for providing data and support. We thank

Robert Schwartz, Trenton Franz, Todd Caldwell, and an anony-

mous reviewer for their constructive comments, which significantly

improved this manuscript. Finally, the editor, Nunzio Romano, is

thanked for guiding the review process.

Edited by: N. Romano


http://www.bris.ac.uk/news/2014/august/soil-moisture-and-cosmic-rays.html

http://www.bris.ac.uk/news/2014/august/soil-moisture-and-cosmic-rays.html


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